In real-time systems, utilization-based schedulability test is a common approach to determine whether or not tasks can be admitted without violating deadline requirements. The test is extremely simple, since it only needs to compare the utilization of the tasks with a predetermined bound. As such, utilization-based schedulability tests are suitable for online use. The challenge is how to derive a reasonable utilization bound for a given system. Most existing results are obtained on a case-by-case basis because of their analytical complexity. In this paper, we develop a flexible and unified representation framework of real-time systems (i.e., tasks and schedulers) based on network calculus techniques. Our representation framework, together with the proposed bound derivation method, leads to a general bound result, which is applicable to a large family of real-time systems.